Proportional Odds Model for Ordinal Regression
Fits the proportional odds model to a (preferably ordered) factor response.
propodds(reverse = TRUE, whitespace = FALSE)
reverse, whitespace |
Logical.
Fed into arguments of the same name in |
The proportional odds model is a special case from the class of
cumulative link models.
It involves a logit link applied to cumulative probabilities and a
strong parallelism assumption.
A parallelism assumption means there is less chance of
numerical problems because the fitted probabilities will remain
between 0 and 1; however
the parallelism assumption ought to be checked,
e.g., via a likelihood ratio test.
This VGAM family function is merely a shortcut for
cumulative(reverse = reverse, link = "logit", parallel = TRUE).
Please see cumulative for more details on this model.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
No check is made to verify that the response is ordinal if the
response is a matrix;
see ordered.
Thomas W. Yee
Agresti, A. (2010). Analysis of Ordinal Categorical Data, 2nd ed. Hoboken, NJ, USA: Wiley.
Yee, T. W. (2010). The VGAM package for categorical data analysis. Journal of Statistical Software, 32, 1–34. https://www.jstatsoft.org/v32/i10/.
Yee, T. W. and Wild, C. J. (1996). Vector generalized additive models. Journal of the Royal Statistical Society, Series B, Methodological, 58, 481–493.
# Fit the proportional odds model, p.179, in McCullagh and Nelder (1989)
pneumo <- transform(pneumo, let = log(exposure.time))
(fit <- vglm(cbind(normal, mild, severe) ~ let, propodds, data = pneumo))
depvar(fit) # Sample proportions
weights(fit, type = "prior") # Number of observations
coef(fit, matrix = TRUE)
constraints(fit) # Constraint matrices
summary(fit)
# Check that the model is linear in let ----------------------
fit2 <- vgam(cbind(normal, mild, severe) ~ s(let, df = 2), propodds, data = pneumo)
## Not run: plot(fit2, se = TRUE, lcol = 2, scol = 2)
# Check the proportional odds assumption with a LRT ----------
(fit3 <- vglm(cbind(normal, mild, severe) ~ let,
cumulative(parallel = FALSE, reverse = TRUE), data = pneumo))
pchisq(deviance(fit) - deviance(fit3),
df = df.residual(fit) - df.residual(fit3), lower.tail = FALSE)
lrtest(fit3, fit) # EasierPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.